MELBOURNE - Serena Williams is a year short of spending a quarter of a century as a professional player but the learning has never stopped for the 23-times Grand Slam winner.

The American held off a strong comeback from world number one Simona Halep during a thrilling 6-1 4-6 6-4 win on Monday to reach the Australian Open quarter-finals.

After being broken in the opening game of the match, Williams won six straight games to claim the set in 20 minutes.

Few would have bet on French Open champion Halep fighting back from that mauling but the Romanian conjured up exceptional grit to force a deciding set.

That proved to be an interesting experience for Williams, who has won 72 WTA singles titles.

"I'm still learning, which is, at my age and my point in my career, I think admirable and exciting that I still have things I can learn from," she told reporters.

"I feel like each day, each match, and each tournament I'm learning something, and I think today I'm just learning that I have to fight for titles. I have to fight for matches."

The 37-year-old took a break from tennis after the birth of her daughter in 2017 and only returned last year. But she showed against Halep she has lost none of her brutal power and athleticism.

"I played really good in that. I don't know if that's the best I have played. I honestly can't remember the matches, but probably," Williams said.

"But that goes to show you that you have to play well for two sets. You can't just play well for one set or six games. You have to bring it every single point, every single game, until the match is literally over."

Williams played her first match on Dec. 31 in the Hopman Cup since her U.S. Open final defeat by Naomi Osaka in September.

She said her progress to the last eight at Melbourne Park does not reflect poorly on the level of competition in women's tennis.

"I think it says more about me than women's tennis. I think it says women's tennis is amazing. It's at the highest level it's ever been," Williams said.

"Of course, I'm the biggest advocate of women's tennis but I really do believe in my heart that everyone is playing well, and it's tough out here."

(Reporting by Sudipto Ganguly; editing by Ed Osmond) ((sudipto.ganguly@thomsonreuters.com; +91 22 6180 7264; Reuters Messaging: sudipto.ganguly.thomsonreuters.com@reuters.net))